Remarks on differential Harnack inequalities
Remarks on differential Harnack inequalities
复制标题
DOI：
10.1016/j.jmaa.2013.07.043
复制
发表时间：
2014
影响因子：
1.3
通讯作者：
B. Qian
中科院分区：
文献类型：
--
作者：
B. Qian
本文推广了李和徐[J.F. [1] Li，X.J. Xu，Differential Harnack inequalities on Riemannian manifold I：linear heat equation，Adv. Math. 226（5）（2011）4456-4491] and Baudoin and Garofalo [F. Baudoin，N. Garofalo，Perelman's entropy and doubling property on Riemannian manifold，J. Geom. Anal. 21（2011）1119-1131]。由此，我们可以得到新的Harnack不等式和新的下界相关联的热核。并给出了一些新的具有单调性的熵公式。
In this paper, we give a generalization of (global and local) differential Harnack inequalities for heat equations obtained by Li and Xu [J.F. Li, X.J. Xu, Differential Harnack inequalities on Riemannian manifolds I: linear heat equation, Adv. Math. 226 (5) (2011) 4456–4491] and Baudoin and Garofalo [F. Baudoin, N. Garofalo, Perelman’s entropy and doubling property on Riemannian manifolds, J. Geom. Anal. 21 (2011) 1119–1131]. From this we can derive new Harnack inequalities and new lower bounds for the associated heat kernel. Also we provide some new entropy formulas with monotonicity.